Search results for " Nonlinear"
showing 10 items of 1224 documents
Sharp Poincaré inequalities in a class of non-convex sets
2018
Let $gamma$ be a smooth, non-closed, simple curve whose image is symmetric with respect to the $y$-axis, and let $D$ be a planar domain consisting of the points on one side of $gamma$, within a suitable distance $delta$ of $gamma$. Denote by $mu_1^{odd}(D)$ the smallest nontrivial Neumann eigenvalue having a corresponding eigenfunction that is odd with respect to the $y$-axis. If $gamma$ satisfies some simple geometric conditions, then $mu_1^{odd}(D)$ can be sharply estimated from below in terms of the length of $gamma$ , its curvature, and $delta$. Moreover, we give explicit conditions on $delta$ that ensure $mu_1^{odd}(D)=mu_1(D)$. Finally, we can extend our bound on $mu_1^{odd}(D)$ to a …
Weak commutation relations of unbounded operators: Nonlinear extensions
2013
We continue our analysis of the consequences of the commutation relation $[S,T]=\Id$, where $S$ and $T$ are two closable unbounded operators. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space $\H$ where the operators act. {We also consider what we call, adopting a physical terminology}, a {\em nonlinear} extension of the above commutation relations.
The three-vertex in the closed half-string field theory and the general gluing and resmoothing theorem
1997
In this letter we prove that the half-string three-vertex in closed string field theory satisfies the general gluing and resmoothing theorem. We also demonstrate how one calculates amplitudes in the half-string approach to closed string field theory, by working out explicitly a few simple three-amplitudes.
Symmetric frames on Lorentzian spaces
1991
Symmetric frames (those whose vectors are metrically indistinguishable) are studied both, from the algebraic and differential points of view. Symmetric frames which, in addition, remain indistinguishable for a given set of concomitants of the metric are analyzed, and the necessary and sufficient conditions for a space‐time to admit them are given. A new version of the cosmological principle then follows. Natural symmetric frames (induced by local charts) are also considered, and the space‐times admitting them are obtained.
Elementary symmetric functions of two solvents of a quadratic matrix equations
2008
Quadratic matrix equations occur in a variety of applications. In this paper we introduce new permutationally invariant functions of two solvents of the n quadratic matrix equation X^2- L1X - L0 = 0, playing the role of the two elementary symmetric functions of the two roots of a quadratic scalar equation. Our results rely on the connection existing between the QME and the theory of linear second order difference equations with noncommutative coefficients. An application of our results to a simple physical problem is briefly discussed.
On the numerical evaluation of algebro-geometric solutions to integrable equations
2011
Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated to real Riemann surfaces. Typical analytical problems in the numerical evaluation of these solutions are studied. In the case of hyperelliptic surfaces efficient algorithms exist even for almost degenerate surfaces. This allows the numerical study of solitonic limits. For general real Riemann surfaces, the choice of a homology basis adapted to the anti-holomorphic involution is important for a convenient formulation of the solutions and smoothness conditions. Since existing algorithms for algebraic curves produce a homology basis no…
Extended pseudo-fermions from non commutative bosons
2013
We consider some modifications of the two dimensional canonical commutation relations, leading to {\em non commutative bosons} and we show how biorthogonal bases of the Hilbert space of the system can be obtained out of them. Our construction extends those recently introduced by one of us (FB), modifying the canonical anticommutation relations. We also briefly discuss how bicoherent states, producing a resolution of the identity, can be defined.
Comments on space–time signature
1993
In terms of three signs associated to two vectors and to a 2-plane, a formula for the signature of any four-dimensional metric is given. In the process, a simple expression for the sign of the Lorentzian metric signature is obtained. The rela- tionship between these results and those already known are commented upon.
Period-multiplying bifurcations and multifurcations in conservative mappings
1983
The authors have investigated numerically and analytically the period-doubling bifurcations and multifurcations of the periodic orbits of the conservative sine-Gordon mappings. They have derived a general equation for the appearance of multifurcations in conservative mappings. In agreement with many recent studies, they also find evidence that such mappings possess universality properties. They also discuss the role of multifurcations in conservative mappings exhibiting chaotic behaviour.
Sato's universal Grassmannian and group extensions
1991
An extension \(\widehat{GL}\) of the symmetry group GL of Sato's universal Grassmannian GM is constructed. The extension plays a similar role to that of the central extension \(\widehat{GL}_{{\text{res}}}\) in the approach of Segal and Wilson to τ functions and KP hierarchy. Our group G contains GLres as a subgroup and the associated τ function is a deformation of the usual τ function, leading to a deformed KP hierarchy. A relation to current algebra of Yang-Mills theory in 3+1 dimension is discussed.